At least, I'm fairly sure there isn't - I have to know the number of electors* in certain areas for work quite often, and we do it by counting them from electoral registers. Literally counting, person by person, takes ages.

If you have geocoded UPRN data you can use that in mapping software to tell you. But if you had access to that, you wouldn't be asking.

the company I used to work for used mapinfo software where you just draw a circle on an OS map and it gives you all the postcodes and the number of addresses at each postcode. it's fucking expensive though - I'm gonna need to become MUCH more successful before I can justify the expense.